The average of four numbers (z+16), (y+15), (y-25) and 1.2z is (y-6). If one more number which is 144 is added then the new average will be (y-1). The value of ‘z’ is what percentage of the value of ‘y’?

Solution

The average of four numbers (z+16), (y+15), (y-25) and 1.2z is (y-6).

(z+16)+(y+15)+(y-25)+1.2z = 4(y-6)    Eq.(i)

If one more number which is 144 is added then the new average will be (y-1).

(z+16)+(y+15)+(y-25)+1.2z+144 = 5(y-1)

Put Eq.(i) in the above equation.

4(y-6)+144 = 5(y-1)

4y-24+144 = 5y-5

5y-4y = 144-24+5

y = 125

Put the value of ‘y’ in Eq.(i).

(z+16)+(125+15)+(125-25)+1.2z = 4(125-6)

(z+16)+140+100+1.2z = 4x119

(z+16)+140+100+1.2z = 476

256+2.2z = 476

2.2z = 476-256 = 220

z = 100

Required percentage = (100/125)x100

= (4/5)x100

= 80%